Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
8001	5^153622-42	107378	Lelio R Paula	02/2017
8002	2^356699-97305	107378	Lelio R Paula	03/2017
8003	13129^26072-26072^13129	107371	Norbert Schneider	09/2022
8004	2^356654+85	107364	Lelio R Paula	11/2011
8005	2^356641-19921	107360	Enzo Doria	06/2013
8006	5*10^107355+11	107356	Robert Price	08/2019
8007	2^356623-465	107355	Lelio R Paula	03/2017
8008	19^83945-92	107345	Lelio R Paula	02/2017
8009	25491^16246+16246^25491	107337	Hans Havermann	11/2020
8010	10^107334+28149	107335	Patrick De Geest	03/2017
8011	10^107334-83	107334	Lelio R Paula	02/2017
8012	2^356518+885	107323	Lelio R Paula	03/2017
8013	(59*10^107322+391)/9	107323	Robert Price	03/2021
8014	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
8015	(2^356468+1162)/2	107308	Stefano Morozzi	09/2020
8016	2^356442-114713	107300	Enzo Doria	04/2015
8017	2^356425+72257	107295	Enzo Doria	04/2016
8018	2^356351-112237	107273	Enzo Doria	06/2014
8020	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
8019	2^356322+74539	107264	Enzo Doria	04/2016
8021	2^356274+1874479	107250	Enzo Doria	06/2016
8022	24606^22819+22819^24606	107241	Hans Havermann	10/2020
8023	(2^356243+3686)/2	107240	Stefano Morozzi	09/2020
8024	20^82422-93	107234	Lelio R Paula	02/2017
8025	2^356157-20365	107214	Enzo Doria	06/2013
8026	8*10^107209+99	107210	Robert Price	03/2021
8027	2^356129-18949	107206	Enzo Doria	05/2013
8028	(15^91163-1)/13873078234414574	107200	Paul Vanderveen	06/2025
8029	2^356100-109587	107197	Enzo Doria	04/2014
8030	165^48333+164	107178	Norbert Schneider	03/2026
8031	2*10^107173-37	107174	Robert Price	11/2021
8032	(2^355978+3262)/2	107160	Stefano Morozzi	02/2021
8033	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
8034	2^355968-64875	107158	Lelio R Paula	01/2017
8035	2^355952+1870321	107153	Enzo Doria	05/2016
8036	27069^9088+9088^27069	107152	Hans Havermann	11/2020
8037	2^355915-117	107142	Lelio R Paula	11/2011
8038	(16*10^107140+77)/3	107141	Robert Price	03/2019
8039	24628^22369+22369^24628	107124	Hans Havermann	11/2020
8040	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
8042	3^224495-8	107112	Lelio R Paula	12/2013
8041	Phi(227687,3)	107112	Henri Lifchitz	12/2025
8043	3*10^107096+23	107097	Robert Price	03/2022
8044	25077^18632+18632^25077	107086	Hans Havermann	10/2020
8045	7^126691-44	107067	Lelio R Paula	03/2017
8046	4^177830-8243	107065	Mike Oakes	02/2011
8047	(509*10^107057+13)/9	107059	Robert Price	05/2022
8048	2^355604+214051	107048	Enzo Doria	10/2023
8049	(2^355562+1702)/2	107035	Stefano Morozzi	09/2020
8050	10^107028+3593037	107029	Paul Bourdelais	10/2021
8051	10^107028-43301	107028	Alfred Reich	08/2024
8052	2^355524-21237	107024	Enzo Doria	06/2013
8054	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
8053	24843^20320+20320^24843	107022	Hans Havermann	10/2020
8055	2^355494-19901	107015	Enzo Doria	06/2013
8056	2^355454-869688105	107003	Lelio R Paula	01/2017
8057	4*10^106997+13	106998	Robert Price	02/2021
8058	(8*10^106985-629)/9	106985	Robert Price	01/2022
8059	2^355366+54615	106976	Lelio R Paula	01/2017
8060	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
8061	2^355275-19861	106949	Enzo Doria	06/2013
8062	27503^7738+7738^27503	106949	Hans Havermann	11/2020
8063	(85*10^106943+77)/9	106944	Robert Price	07/2022
8064	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
8065	4*10^106914-93	106915	Robert Price	07/2020
8066	(151^49069-1)/90910031243271150	106904	Paul Vanderveen	06/2025
8067	4*10^106892-3	106893	Robert Price	10/2015
8068	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
8069	2^355001+335931	106866	Enzo Doria	08/2024
8070	2^354946-3	106850	M. Frind & P. Underwood	08/2002
8071	(2^354945+3134)/2	106849	Stefano Morozzi	09/2020
8072	(46^64384+1)/(46^128+1)	106843	Martin Hopf	12/2023
8073	2^354873-18693	106828	Enzo Doria	05/2013
8074	(2^354831+3186)/2	106815	Stefano Morozzi	09/2020
8076	2^354828+4257	106814	Lelio R Paula	01/2017
8075	25216^17217+17217^25216	106814	Hans Havermann	10/2020
8077	(2^354799+1218)/2	106805	Stefano Morozzi	09/2020
8078	436^40459+40459^436	106791	Norbert Schneider	03/2019
8079	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
8080	(115*10^106772-7)/9	106774	Robert Price	02/2020
8081	2^354640-354640+1	106758	Robert Price	10/2014
8082	(2^354603+2606)/2	106746	Stefano Morozzi	09/2020
8083	2^354585+95	106741	Lelio R Paula	10/2011
8084	(206*10^106737+1)/9	106739	Robert Price	04/2022
8085	2^354553+189	106732	Lelio R Paula	10/2011
8087	(2^354546+1338)/2	106729	Stefano Morozzi	02/2021
8086	(8*10^106729-71)/9	106729	Serge Batalov	11/2022
8088	2^354514-109031	106720	Enzo Doria	04/2014
8089	2^354509-109465	106718	Enzo Doria	04/2014
8090	fibonacci(510628)+2	106715	Jon Grantham	08/2023
8091	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
8092	Phi(217618,10)/899798636917	106693	Makoto Kamada	06/2019
8093	15^90710+28	106684	Lelio R Paula	04/2017
8094	7^126237+34	106683	Lelio R Paula	03/2017
8095	2^354385-115315	106681	Enzo Doria	06/2015
8096	2^354327-19305	106664	Enzo Doria	06/2013
8097	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
8098	10^106636+97	106637	Lelio R Paula	02/2017
8099	10^106636-22923	106636	Patrick De Geest	03/2017
8100	2^354220-57	106631	Lelio R Paula	10/2011
8101	(68*10^106628-329)/9	106629	Robert Price	03/2021
8102	(29*10^106620-77)/3	106621	Robert Price	02/2020
8103	(746*10^106618+1)/9	106620	Robert Price	03/2020
8104	2*10^106613+29	106614	Robert Price	02/2021
8105	2^354157-17041	106612	Enzo Doria	05/2013
8106	12^98778+73	106600	Lelio R Paula	02/2017
8107	Phi(447629,-2)	106594	Henri Lifchitz	12/2025
8108	33333^1576+1576^33333	106585	Hans Havermann	11/2020
8109	2^354064+1870651	106584	Enzo Doria	05/2016
8110	24568^21779+21779^24568	106577	Hans Havermann	11/2020
8111	2^353992-57	106563	Lelio R Paula	10/2011
8112	9*10^106559+59	106560	Robert Price	01/2020
8113	7*10^106553+27	106554	Robert Price	11/2020
8114	28847^4938+4938^28847	106548	Hans Havermann	10/2020
8115	(20^81901-1)/42030774209	106546	Paul Vanderveen	06/2025
8117	NSW(139160)	106535	Robert Price	12/2018
8116	f(278321)	106535	Robert Price	07/2023
8118	(7*10^106516+113)/3	106517	Robert Price	02/2018
8119	2^353832-1853849	106515	Enzo Doria	09/2015
8122	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
8120	Phi(126037,7)	106513	Henri Lifchitz	12/2025
8121	Phi(252074,-7)	106513	Henri Lifchitz	02/2026
8123	2^353794-18453	106503	Enzo Doria	05/2013
8124	(2^353761+2094)/2	106493	Stefano Morozzi	09/2020
8125	2^353728+7695	106483	Lelio R Paula	01/2017
8126	26476^10509+10509^26476	106475	Hans Havermann	10/2020
8127	2^353672-303	106466	Yves Minet	02/2012
8128	6^136811+101	106460	Lelio R Paula	02/2017
8129	2^353641+1871981	106457	Enzo Doria	05/2016
8130	(8*10^106454-29)/3	106455	Robert Price	07/2018
8131	27845^6654+6654^27845	106454	Hans Havermann	11/2020
8132	10^106449-700001	106449	Robert Price	08/2021
8133	25316^16017+16017^25316	106444	Hans Havermann	11/2020
8134	2^353553+54615	106431	Lelio R Paula	01/2017
8135	2^353544-18897	106428	Enzo Doria	05/2013
8136	28894^4823+4823^28894	106426	Hans Havermann	11/2020
8137	(19*10^106422+29)/3	106423	Robert Price	12/2021
8138	(694*10^106418+53)/9	106420	Robert Price	02/2022
8139	6*10^106412-13	106413	Robert Price	07/2022
8140	25696^13829+13829^25696	106402	Hans Havermann	11/2020
8141	6^136729-133	106396	Lelio R Paula	02/2017
8142	2^353418+1605	106390	Lelio R Paula	01/2017
8143	2^353387+65	106381	Lelio R Paula	10/2011
8144	2^353372+74311	106376	Enzo Doria	04/2016
8145	2^353344-3693	106368	Yves Minet	03/2017
8146	(772*10^106365-7)/9	106367	Robert Price	06/2022
8147	(56*10^106351+619)/9	106352	Robert Price	05/2021
8149	2^353277-20089	106347	Enzo Doria	06/2013
8148	2^353275+72173	106347	Enzo Doria	04/2016
8150	2^353268-17705	106345	Enzo Doria	05/2013
8151	2^353267-19857	106344	Enzo Doria	06/2013
8152	(46*10^106343+143)/9	106344	Robert Price	01/2019
8154	(2^353189+3054)/2	106321	Stefano Morozzi	09/2020
8153	35087^1072+1072^35087	106321	Hans Havermann	10/2020
8155	(2^353184+1290)/2	106319	Stefano Morozzi	01/2021
8156	F(508799)/24738824977/1990778864897	106310	Serge Batalov	07/2024
8157	26985^8684+8684^26985	106287	Hans Havermann	10/2020
8158	(2^353051+606)/2	106279	Stefano Morozzi	09/2020
8160	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
8159	(46*10^106277+107)/9	106278	Robert Price	06/2022
8161	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
8162	2^353025+72257	106272	Enzo Doria	04/2016
8165	2^352932-20345	106244	Enzo Doria	06/2013
8163	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
8164	25628^13983+13983^25628	106244	Hans Havermann	10/2020
8166	2^352883-187	106229	Lelio R Paula	10/2011
8167	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
8168	(55*10^106222+377)/9	106223	Robert Price	02/2019
8169	2^352814-131	106208	Lelio R Paula	10/2011
8170	2^352752+73951	106189	Enzo Doria	04/2016
8171	11876*25^75945+357	106171	Eric Chen	10/2023
8172	6^136434+5	106167	Lelio R Paula	11/2014
8173	25296^15737+15737^25296	106166	Hans Havermann	09/2020
8174	8*10^106157-13	106158	Robert Price	08/2019
8175	2^352641+225677	106156	Enzo Doria	08/2024
8176	7*5^151872-8	106155	Lelio R Paula	11/2014
8177	105^52520-2	106153	Lelio R Paula	10/2017
8178	(23*10^106152-29)/3	106153	Robert Price	03/2022
8179	2^352601-1604809	106144	Enzo Doria	05/2015
8180	12^98353-43	106141	Lelio R Paula	02/2017
8181	2^352585-18901	106139	Enzo Doria	05/2013
8182	26363^10614+10614^26363	106135	Hans Havermann	09/2020
8183	(2^352554-3)/193	106128	Lelio R Paula	12/2013
8184	2^352540+15015	106126	Lelio R Paula	01/2017
8185	25068^17119+17119^25068	106125	Hans Havermann	09/2020
8186	2^352524-3149	106121	Yves Minet	10/2014
8187	(7*10^106119-67)/3	106120	Robert Price	10/2021
8188	2^352486-1858781	106109	Enzo Doria	04/2016
8189	2^352444+12705	106097	Lelio R Paula	01/2017
8190	28561^5182+5182^28561	106090	Hans Havermann	10/2020
8191	(182*10^106083+43)/9	106085	Robert Price	02/2020
8192	(266*10^106066+1)/3	106068	Robert Price	04/2020
8193	(7*10^106066-187)/9	106066	Tyler Busby	01/2023
8194	2^352228-18953	106032	Enzo Doria	05/2013
8195	(2^352223+1118)/2	106030	Stefano Morozzi	09/2020
8196	(2^352212+2250)/2	106027	Stefano Morozzi	01/2021
8197	(2^352136+2638)/2	106004	Stefano Morozzi	09/2020
8198	2^352107+1872533	105995	Enzo Doria	05/2016
8199	(2^352096+2086)/2	105992	Stefano Morozzi	09/2020
8200	2^352066-2591	105983	Yves Minet	07/2014
8201	2^352030+715	105972	Lelio R Paula	10/2011
8202	9*6^136176-5	105967	Lelio R Paula	11/2014
8203	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
8204	122^50789-50789^122	105965	Norman Luhn	09/2024
8205	28582^5097+5097^28582	105963	Hans Havermann	09/2020
8206	155^48377+2	105962	Lelio R Paula	08/2013
8207	(23*10^105944-119)/3	105945	Robert Price	07/2021
8208	2^351865+1869707	105922	Enzo Doria	05/2016
8209	24974^17427+17427^24974	105921	Hans Havermann	09/2020
8210	25163^16194+16194^25163	105920	Hans Havermann	09/2020
8211	2^351831+23	105912	Lelio R Paula	10/2011
8212	(2^351818+3798)/2	105908	Stefano Morozzi	02/2021
8213	9*2^351784-5	105899	Lelio R Paula	09/2014
8214	(2^351776+2766)/2	105895	Stefano Morozzi	01/2021
8215	(85*10^105881+203)/9	105882	Robert Price	09/2020
8216	2^351671-112387	105864	Enzo Doria	06/2014
8217	2^351669-109501	105863	Enzo Doria	04/2014
8218	2^351644+74731	105856	Enzo Doria	04/2016
8219	13^95025-42	105853	Lelio R Paula	12/2016
8220	2^351599+15015	105842	Lelio R Paula	01/2017
8221	19^82763+90	105834	Lelio R Paula	01/2017
8222	(205*10^105831-1)/3	105833	Robert Price	11/2021
8223	26050^11551+11551^26050	105832	Hans Havermann	09/2020
8224	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
8225	20^81329-51	105812	Lelio R Paula	01/2017
8226	(5*10^105811+211)/9	105811	Robert Price	02/2018
8227	2^351483+28425	105807	Lelio R Paula	01/2017
8228	25231^15610+15610^25231	105804	Hans Havermann	09/2020
8229	15^89960+86	105802	Lelio R Paula	02/2017
8230	2^351460-17289	105801	Enzo Doria	05/2013
8231	19^82735+22	105798	Lelio R Paula	01/2017
8232	2^351435-109077	105793	Enzo Doria	04/2014
8233	2^351393+1089	105780	Lelio R Paula	01/2017
8234	2^351364+72631	105772	Enzo Doria	04/2016
8235	(2^351333+3626)/2	105762	Stefano Morozzi	09/2020
8236	26818^8783+8783^26818	105761	Hans Havermann	09/2020
8239	2^351305+1872467	105754	Enzo Doria	05/2016
8238	3^221649+16	105754	Lelio R Paula	11/2016
8237	32511^1790+1790^32511	105754	Hans Havermann	09/2020
8240	8*3^221637-5	105749	Lelio R Paula	09/2014
8241	2^351279-2780449	105746	Enzo Doria	03/2016
8242	(2^351263+3198)/2	105741	Stefano Morozzi	09/2020
8243	15^89903-26	105735	Lelio R Paula	02/2017
8245	2^351213-73	105726	Lelio R Paula	10/2011
8244	(2^351214+1210)/2	105726	Stefano Morozzi	09/2020
8246	2^351192-4589	105720	Yves Minet	07/2011
8247	20^81250-33	105709	Lelio R Paula	12/2016
8248	(2^351133+3530)/2	105702	Stefano Morozzi	09/2020
8249	(2^351103+534)/2	105693	Stefano Morozzi	09/2020
8250	2^351076-113159	105685	Enzo Doria	07/2014

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